A (partially) bio-based short-chain polyester is prepared through interfacial polycondensation of furan-functionalized diphenolic acid with terephthalic chloride. The furan groups along the backbone of the obtained polyester are able to form a covalent network (PE-fur/Bism) with various ratios of 1,1′-(methylenedi-4,1-phenylene)bismaleimide via the thermoreversible Diels–Alder (DA) reaction. Several techniques have been employed to characterize the polyester network, including 1H-NMR, gel permeation chromatography (GPC), thermogravimetric analysis (TGA), differential scanning calorimetry (DSC), and dynamic mechanical thermal analysis (DMTA). The polyester base polymer displays a glass transition temperature of 115 °C, whereas the temperatures at which the retro-Diels–Alder (rDA) reaction takes place lie above 130 °C for the various polyester/bismaleimide networks. Excellent thermoreversibility and recyclability of the polyester resin have been shown through DSC and DMTA measurements.